with
\(C_{\bar{\Delta }}=(M-2)\pi ^{\frac{M-2}{2}}/((M-2)/2)!\) .[1]}
By changing integration variable from (\(R\) , \(x_{\alpha }^{1}\) ) to
(\(L_{\alpha x}\) , \(x_{\alpha }^{1}\) ), we have,
\(\bar{\Delta }(L_{\alpha x},x_{\alpha }^{(1)},x_{\alpha }^{(M)})dL_{\alpha x}dx_{\alpha }^{(1)}\propto C_{\bar{\Delta }}L_{\alpha x}(L_{\alpha x}^{2}-(x_{\alpha }^{(1)}-x_{\alpha }^{(M)})^{2}\frac{M}{M-1})^{\frac{M-4}{2}}dL_{\alpha x}dx_{\alpha }^{(1)}, \) 
